First, the OCP (REF )
has \(n_x + n_u + (n_x + n_x^2)/2\)  optimization variables at each prediction stage, structurally equivalent to OCPs arising from a direct multiple shooting discretization [1]}. For this set of problems, among the most competitive solvers at the time of this writing are interior point algorithms exploiting the block-sparse structure of the multiple shooting approach [2]}.
Still, these algorithms' cubic computational complexity in the number of shooting nodes leads to a total computational complexity of \(\mathcal {O}(n_x^6)\) , which becomes prohibitive even for a moderate number of states.
